It's not about "one overriding idea", it's about having a fundamental, unified understanding. Edison was about randomly trying things and see what works, Tesla was about seeking fundamental understanding and predicting what will work.

Picking on Tesla for some error given what he did with the AC motor and other projects is very wrongheaded. You're depending on Tesla right now in many ways. Obviously he was wildly successful; Edison's contributions have all fallen by the wayside.